Structural buildings in k-valued logic optoelectronic display information devices

DOI №______

Abstract

The ways of hardware implementation of digital logic elements based on k-valued logic, used in systems of information display of telecommunication equipment for increasing the speed of data processing are offered. The possibility of using a multiplexer circuit as a logical basis in the general case for k-valued logic and for a triple logic in a separate case is shown. On the example of the ternary logic, the possible use of a direct and inverse multiplexer as a complete logical basis is mathematically justified. Using this basis, any complex kvalued logical function can be represented as a multi-tier hierarchical structure in which the element is an elementary multiplexer. The use of multiplexers simplifies the design and synthesis of complex digital circuits with a large number of input variables. The variants of the structural scheme of the ternary full sequential adder using a multiplexer with a single control signal are proposed. To reduce hardware costs and reduce power consumption, an adder circuit has been developed based on a multiplexer with two control signals. To implement a digital element with memory, a block diagram of the ternary D - trigger has been developed using the k- value multiplexer as a basic element. An example of building a digital automaton in a 3-value logic is given, which from a sequence of input signals detects a given combination and provides an output control signal. The proposed method for constructing circuits of digital combinational devices and logical devices with memory based on k -digit multiplexers will allow increasing the capacity and speed of processing large data arrays.

Keywords: K-valued logic, logic base of k-valued logic, ternary logic function, multiplexer, digital automaton of ternary logic, digital combinational devices.

References (MLA)
1. Yablonskiy S. V. Introduction to Discrete Mathematics: a Textbook for High Schools. Moscow: Vysshaya Shkola, 2006. Print.
2. Zakrevskiy A. D., Potosina Yu. V., Cheremisinova L. D. Logical Foundations of the Design of Discrete Devices. Moscow: Fizmatlit, 2007. Print.
3. Miller D. "Multiple Valued Logic: Concepts and Representations: Synthesis Lectures on Digital Circuits and Systems." Morgan & Claypool Publishers (2008): 41-42. Print.
4. Yartsev V. P. "Methods of Forming a Quasi-Two-Dimensional Information Model of the LED Scale." / Telekomunikatsiini ta Informatsiini Tekhnolohii 1 (2014): 86-93. Print.
5. Lobanov L. P., Yaskevich V. O. "Construction of Digital Circuits on Multiplexers." ComputerIntegrated Technologies: Education, Science, Production 8 (2012): 16-21. Print.
6. Dmitrienko V. D., Leonov S. Yu., Gladkikh T. V. "Research Digital Devices by Means of a Modeling System Based on the K-value Differential Calculus." Radioelectronics & Informatics 1 (2008): 63-69. Print.
7. Maslov S. P. " Trinity Circuitry." Prjgramnyˋye sistemyˋ i instrumentyˋ. 13 (2012): 152-158. Print.
8. Patent RU №2394366 С1. Threshold Element of Ternary Logic and Device on its Basis. / Maslov S. P. Registered: Jule 10, 2010 // Bul. 23. Print.
9. Patent RU № 2510129 С1. Trinity D-trigger. / Maslov S. P. Registered: March 20, 2014 // Bul.19. Print.